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Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation

The approach to the solving of gradient problems of parameters identification of quasiideal fields with using applied quasipotential tomographic data based on numerical complex analysis methods is transferred to cases of anisotropic media. We, similar to the existing works of world scientists, some...

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Datum:2018
Hauptverfasser: Bomba, Andriy, Boichura, Myhailo
Format: Artikel
Sprache:Englisch
Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2018
Online Zugang:http://mcm-math.kpnu.edu.ua/article/view/159249
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Назва журналу:Mathematical and computer modelling. Series: Physical and mathematical sciences

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Mathematical and computer modelling. Series: Physical and mathematical sciences
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author Bomba, Andriy
Boichura, Myhailo
author_facet Bomba, Andriy
Boichura, Myhailo
author_sort Bomba, Andriy
baseUrl_str
collection OJS
datestamp_date 2019-03-13T10:33:12Z
description The approach to the solving of gradient problems of parameters identification of quasiideal fields with using applied quasipotential tomographic data based on numerical complex analysis methods is transferred to cases of anisotropic media. We, similar to the existing works of world scientists, some additional information about the nature of the distribution of conductivity inside the domain (research object) is considered a priori known. However, in opposite to the traditional approaches to the statement and solving the problems of electrical impedance tomography, we set the local velocities distribution of a substance (liquid, current) in addition to the averaged potential at the contact sections of plate and body and at other sections (stream lines), we set the potential distribution (according to experimental data, which we approximate using splines, Bezier curves, etc.). Generation of initial data at the boundary of the investigated object is carried out in accordance with the polar model of current injection and a given sum of eigenvalues of the conductivity tensor of the medium. The presence of this kind of data greatly accelerates the process of further solving the problem, which is convenient, in particular, when verifying the method that developed by authors. The corresponding problem is reduced to the iterative solving of a series of problems for the Laplace type equations, where instead of «boundary numerical analogues of the Cauchy-Riemann type equations» appear the ratio of quasiorthogonality with using special types of optimization conditions. In particular: the minimizing functional is constructed by taking into account the Cauchy-Riemann type conditions, the relation between eigenvalues of corresponding anisotropy tensor and also regularizing term; the condition-restriction is built based on ellipticity conditions.
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institution Mathematical and computer modelling. Series: Physical and mathematical sciences
language English
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spelling mcm-mathkpnueduua-article-1592492019-03-13T10:33:12Z Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation Bomba, Andriy Boichura, Myhailo The approach to the solving of gradient problems of parameters identification of quasiideal fields with using applied quasipotential tomographic data based on numerical complex analysis methods is transferred to cases of anisotropic media. We, similar to the existing works of world scientists, some additional information about the nature of the distribution of conductivity inside the domain (research object) is considered a priori known. However, in opposite to the traditional approaches to the statement and solving the problems of electrical impedance tomography, we set the local velocities distribution of a substance (liquid, current) in addition to the averaged potential at the contact sections of plate and body and at other sections (stream lines), we set the potential distribution (according to experimental data, which we approximate using splines, Bezier curves, etc.). Generation of initial data at the boundary of the investigated object is carried out in accordance with the polar model of current injection and a given sum of eigenvalues of the conductivity tensor of the medium. The presence of this kind of data greatly accelerates the process of further solving the problem, which is convenient, in particular, when verifying the method that developed by authors. The corresponding problem is reduced to the iterative solving of a series of problems for the Laplace type equations, where instead of «boundary numerical analogues of the Cauchy-Riemann type equations» appear the ratio of quasiorthogonality with using special types of optimization conditions. In particular: the minimizing functional is constructed by taking into account the Cauchy-Riemann type conditions, the relation between eigenvalues of corresponding anisotropy tensor and also regularizing term; the condition-restriction is built based on ellipticity conditions. Кам'янець-Подільський національний університет імені Івана Огієнка 2018-11-28 Article Article Рецензована Стаття application/pdf http://mcm-math.kpnu.edu.ua/article/view/159249 10.32626/2308-5878.2018-18.14-24 Mathematical and computer modelling. Series: Physical and mathematical sciences; 2018: Mathematical and computer modelling. Series: Physical and mathematical sciences. Issue 18; 14-24 Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки; 2018: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 18; 14-24 2308-5878 10.32626/2308-5878.2018-18 en http://mcm-math.kpnu.edu.ua/article/view/159249/158543 Авторське право (c) 2021 Andriy Bomba, Myhailo Boichura
spellingShingle Bomba, Andriy
Boichura, Myhailo
Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title_full Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title_fullStr Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title_full_unstemmed Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title_short Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation
title_sort numerical complex analysis method for parameters identification of anisotropic media using applied quasipotential tomographic data. part 1: problem statement and its approximation
url http://mcm-math.kpnu.edu.ua/article/view/159249
work_keys_str_mv AT bombaandriy numericalcomplexanalysismethodforparametersidentificationofanisotropicmediausingappliedquasipotentialtomographicdatapart1problemstatementanditsapproximation
AT boichuramyhailo numericalcomplexanalysismethodforparametersidentificationofanisotropicmediausingappliedquasipotentialtomographicdatapart1problemstatementanditsapproximation

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